Multivariate Regime Switching Research Articles

Underlying Inflation and Asymmetric Risks

Abstract We propose a new measure of underlying inflation that informs, in real time, about asymmetric risks on the outlook of inflationary pressures. The asymmetries are generated through nonlinearities induced by economic activity. The new indicator is based on a multivariate regime-switching framework jointly estimated on disaggregated sub-components of the euro area HICP and has several additional advantages. First, it is able to swiftly infer abrupt changes in underlying inflation. Second, it helps to timely track turning points in underlying inflation. Third, the proposed indicator also has a satisfactory performance with respect to various criteria relevant for inflation monitoring.

Maximum Likelihood Estimation of Multivariate Regime Switching Student‐t Copula Models

SummaryWe propose a multivariate regime switching model based on a Student‐ copula function with parameters controlling the strength of correlation between variables and that are governed by a latent Markov process. To estimate model parameters by maximum likelihood, we consider a two‐step procedure carried out through the Expectation–Maximisation algorithm. To address the main computational burden related to the estimation of the matrix of dependence parameters and the number of degrees of freedom of the Student‐ copula, we show a novel use of the Lagrange multipliers, which simplifies the estimation process. The simulation study shows that the estimators have good finite sample properties and the estimation procedure is computationally efficient. An application concerning log‐returns of five cryptocurrencies shows that the model permits identifying bull and bear market periods based on the intensity of the correlations between crypto assets.

Portfolio Optimization on Multivariate Regime-Switching GARCH Model with Normal Tempered Stable Innovation

This paper uses simulation-based portfolio optimization to mitigate the left tail risk of the portfolio. The contribution is twofold. (i) We propose the Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) to accommodate fat tails, volatility clustering and regime switch. The volatility of each asset independently follows the regime-switch GARCH model, while the correlation of joint innovation of the GARCH models follows the Hidden Markov Model. (ii) We use tail risk measures, namely conditional value-at-risk (CVaR) and conditional drawdown-at-risk (CDaR), in the portfolio optimization. The optimization is performed with the sample paths simulated by the MRS-MNTS-GARCH model. We conduct an empirical study on the performance of optimal portfolios. Out-of-sample tests show that the optimal portfolios with tail measures outperform the optimal portfolio with standard deviation measure and the equally weighted portfolio in various performance measures. The out-of-sample performance of the optimal portfolios is also more robust to suboptimality on the efficient frontier.

Multivariate Regime Switching GARCH Model Application to Portfolio and Risk Management

Regime switching dynamic correlation (RSDC) model allows the correlations to be constant with the regimes themselves however, it differs across regimes. RSDC model has retained many good properties from CCC multivariate GARCH and DCC multivariate GARCH. For example, RSDC does not suffer from the curse of dimensional due to the two steps estimation for volatility. Positive semi definite is also easy to achieve from its decomposition from covariances. In this research, the feasibility of the constant correlations assumptions have been tested using Lagrange Multiplier test developed by Tse (2000) on the RSDC model.

Regime switching dynamic correlations for asymmetric and fat-tailed conditional returns

A non-Gaussian multivariate regime switching dynamic correlation model for financial asset returns is proposed. It incorporates the multivariate generalized hyperbolic law for the conditional distribution of returns. All model parameters are estimated consistently using a new two-stage expectation–maximization algorithm that also allows for incorporation of shrinkage estimation via quasi-Bayesian priors. It is shown that use of Markov switching correlation dynamics not only leads to highly accurate risk forecasts, but also potentially reduces the regulatory capital requirements during periods of distress. In terms of portfolio performance, the new regime switching model delivers consistently higher Sharpe ratios and smaller losses than the equally weighted portfolio and all competing models. Finally, the regime forecasts are employed in a new dynamic risk control strategy that avoids most losses during the financial crisis and vastly improves risk-adjusted returns.

A Flexible Regime Switching Model for Asset Returns

A non-Gaussian multivariate regime switching dynamic correlation model for fi nancial asset returns is proposed. It incorporates the multivariate generalized hyperbolic law for the conditional distribution of returns. All model parameters are estimated consistently using a new two-stage expectation-maximization algorithm that also allows for incorporation of shrinkage estimation via quasi-Bayesian priors. It is shown that use of Markov switching correlation dynamics not only leads to highly accurate risk forecasts, but also potentially reduces the regulatory capital requirements during periods of distress. In terms of portfolio performance, the new regime switching model delivers consistently higher Sharpe ratios and smaller losses than the equally weighted portfolio and all competing models. Finally, the regime forecasts are employed in a dynamic risk control strategy that avoids most losses during the fi nancial crisis and vastly improves risk-adjusted returns.

Forecasting US interest rates and business cycle with a nonlinear regime switching VAR model

AbstractThis paper introduces a regime switching vector autoregressive model with time‐varying regime probabilities, where the regime switching dynamics is described by an observable binary response variable predicted simultaneously with the variables subject to regime changes. Dependence on the observed binary variable distinguishes the model from various previously proposed multivariate regime switching models, facilitating a handy simulation‐based multistep forecasting method. An empirical application shows a strong bidirectional predictive linkage between US interest rates and NBER business cycle recession and expansion periods. Due to the predictability of the business cycle regimes, the proposed model yields superior out‐of‐sample forecasts of the US short‐term interest rate and the term spread compared with the linear and nonlinear vector autoregressive (VAR) models, including the Markov switching VAR model.

다변량 국면전환과 위기를 고려한 국제경기변동의 구조적 변화 추정

다변량 국면전환과 위기를 고려한 국제경기변동의 구조적 변화 추정

Asset allocation and regime switching on Croatian financial market

It has been known for quite some time now that financial markets exhibit changes in regimes over time. A majority of the literature tends to support that financial markets undergo regimes of bull and bear markets. This characteristic should be modeled in a proper way as investors are always interested in beating the market: either by achieving better returns than others, or by minimizing their portfolio risks. There exist many mathematical and statistical models that are used as tools to achieve the mentioned goals. Introducing the regime switching methodology in existing models has proven to be facilitate achieving such goals. Therefore, the objective of this study is to utilize the regime switching methodology on the Croatian financial market to ascertain its usefulness for Croatian investors. Multivariate regime switching and non-switching models were estimated using daily data from the period 2 January 2007 to 31 December 2015. The assumption is that the investor is interested in stock and bond markets. The results from the MGARCH and regime switching MGARCH models are then compared in order to give answers as to whether the respective methodology applied to the Croatian market is useful and how it may benefit investors. Most of the results support the presumption of incorporating this particular methodology in financial modeling for the Croatia markets. This is the first research that applies the regime switching MGARCH methodology in Croatia (including the Balkan region), hence we expect that this will be a significant contribution to existing methodologies in literature.

Nonlinear Relationship Between Permanent and Transitory Components of Monetary Aggregates and the Economy

This paper uses several methods to study the interrelationship among Divisia monetary aggregates, prices, and income, allowing for nonstationary, nonlinearities, asymmetries, and time-varying relationships among the series. We propose a multivariate regime switching unobserved components model to obtain transitory and permanent components for each series, allowing for potential recurrent and structural changes in their dynamics. Each component follows distinct two-state Markov processes representing low or high phases. Since the lead-lag relationship between the phases can vary over time, rather than pre-imposing a structure to their linkages, the proposed flexible framework enables us to study their specific lead-lag relationship over each one of their cycles and over each U.S. recession in the last 40 years. The decomposition of the series into permanent and transitory components reveals striking results. First, we find a strong nonlinear association between the components of money and prices—all low phases of the transitory component of prices were preceded by tight transitory and permanent money phases. We also find that most recessions were preceded by tight money phases (its cyclical and permanent components) and high transitory price phases (with the exception of the 2001 and 2009-2010 recessions). In addition, all recessions were associated with a decrease in transitory and permanent income.

A Multivariate Regime-Switching Mean Reverting Process and Its Application to the Valuation of Credit Risk

In this article, we study the counterparty risk on a credit default swap (CDS) and the valuation of a first-to-default basket swap on three underlyings under a common shock model with regime-switching intensities. We assume that the defaults of all the names are driven by some shock events, whose arrivals are governed by a multivariate regime-switching shot noise process. Based on some expressions for the joint Laplace transform of the regime-switching shot noise processes, we give explicit formulas for the spread of the CDS contract with and without counterparty risk and the spread of the first-to-default basket swap on the three underlyings.

On the relationship between the prices of oil and the precious metals: Revisiting with a multivariate regime-switching decision tree

This study examines the volatility and correlation and their relationships among the euro/US dollar exchange rates, the S&P500 equity indices, and the prices of WTI crude oil and the precious metals (gold, silver, and platinum) over the period 2005 to 2012. Our model links the univariate volatilities with the correlations via a hidden stochastic decision tree. The ensuing Hidden Markov Decision Tree (HMDT) model is in fact an extension of the Hidden Markov Model (HMM) introduced by Jordan et al. (1997). The architecture of this model is the opposite that of the classical deterministic approach based on a binary decision tree and, it allows a probabilistic vision of the relationship between univariate volatility and correlation. Our results are categorized into three groups, namely (1) exchange rates and oil, (2) S&P500 indices, and (3) precious metals. A switching dynamics is seen to characterize the volatilities, while, in the case of the correlations, the series switch from one regime to another, this movement touching a peak during the period of the Subprime crisis in the US, and again during the days following the Tohoku earthquake in Japan. Our findings show that the relationships between volatility and correlation are dependent upon the nature of the series considered, sometimes corresponding to those found in econometric studies, according to which correlation increases in bear markets, at other times differing from them.

Modelling Sovereign Ratings Impacts on Stock Return Distributions within a Multivariate Regime Switching Long Memory Framework

We develop a framework that allows a multivariate system of long memory processes to be conditional on specific regimes to investigate the effects of credit rating agencies (CRAs)’ sovereign credit re-ratings on European stock and currency return distributions via their first four realized moments. We find heterogeneous effects of sovereign rating actions across regimes, supporting the usefulness of our proposed model in accommodating both long memory and regime switching features. Furthermore, we reveal that the total effects (both direct and indirect forces) of sovereign credit assessments on the realized moments can be different to their direct effects on individual moments. We find that the rank orders of CRAs are not unique across rating regimes nor for each realized moment.

Interest rate pass-through in the Euro area during the financial crisis: A multivariate regime-switching approach

In this paper we use a Markov-switching vector autoregressive model to analyse the interest rate pass-through between interbank and retail bank rates in the Euro area. Empirical results, based on monthly data for the period 2003–2011, show that during periods of financial distress bank lending rates to both households and non-financial corporations show a reduction of their degree of pass-through from the money market rate. Significant sectoral heterogeneities characterise the transmission mechanism of monetary policy impulses, with rates on loans to non-financial firms being more affected by changes in the interbank rate than loans to households, both in times of high volatility and in normal market conditions.

Multivariate Regime Switching Model with Flexible Threshold Variable: With an Application to Returns from a Portfolio of U.S. Stocks

This paper proposes a novel multivariate regime switching model that allows the threshold variable to be a linear combination of covariates with unknown coefficients: the model is likely to be more suitable to analyze time series of data in which regimes dynamics are driven by multiple covariates rather than by just one single threshold variable. The paper considers least squares estimation of the model and it proposes a test for the number of regimes based on theoretical results from multivariate statistics. Finite sample results from Monte Carlo analysis strengthen the methodological contribution of the paper. An application to measuring regime-specific cross-sectional dependence in the U.S. stock market illustrates the usefulness of the proposed model for applied work.

Nonlinear Relationship Between Permanent and Transitory Components of Monetary Aggregates and the Economy

This paper uses several methods to study the interrelationship among Divisia monetary aggregates, prices, and income; allowing for non-stationary, non-linearities, asymmetries, and time-varying relationships among the series. We propose a multivariate regime switching unobserved components model to obtain transitory and permanent components for each series, allowing for potential recurrent and structural changes in their dynamics. Each component follows distinct two-state Markov processes representing low or high phases. Since the lead-lag relationship between the phases can vary over time, rather than preimposing a structure to their linkages, the proposed flexible framework enables us to study their specific lead-lag relationship over each one of their cycles and over each U.S. recession in the last 40 years. The decomposition of the series into permanent and transitory components reveals striking results. First, we find a strong nonlinear association between the components of money and prices – all low phases of the transitory component of prices were preceded by tight transitory and permanent money phases. We also find that most recessions were preceded by tight money phases, (its cyclical and permanent components), and high transitory price phases, (with the exception of the 2001 and 2009-2010 recessions). In addition, all recessions were associated with a decrease in transitory and permanent income.

Moments of multivariate regime switching with application to risk-return trade-off

Abstract We use a Fourier transform to derive multivariate conditional and unconditional moments of multi-horizon returns under a regime-switching model. These moments are applied to examine the relevance of risk horizon and regimes for buy-and-hold investors. We analyze the impact of time-varying expected returns and risk (variance and covariance) on portfolio allocations' “term structure”—portfolio allocations as a function of the investment horizon. Using monthly observations on S&P composite index and 10-year Government Bond, we find that the term structure of the optimal allocations depends on market conditions measured by the probability of being in bull state. At short horizons and when this probability is low, buy-and-hold investors decrease their holdings of risky assets. We also find that the conditional optimal portfolio performs quite well at short and intermediate horizons and less at long horizons.

Cross hedging single stock with American Depositary Receipt and stock index futures

This paper investigates the cross hedging effectiveness of individual stock in a market that does not have single stock futures traded using American Depositary Receipt (ADR) and stock index futures. We apply Caporin and Billio’s Multivariate regime switching GARCH to capture the state-dependent covariance structure of underlying stock, ADR and stock index futures. Empirical results indicate that in general simultaneous hedging with both ADR and index futures creates hedging gains and incorporating regime switching effects further increases the hedging performances.

Modeling International Financial Returns with a Multivariate Regime-switching Copula

In order to capture observed asymmetric dependence in international financial returns, we construct a multivariate regime-switching model of copulas. We model dependence with one Gaussian and one canonical vine copula regime. Canonical vines are constructed from bivariate conditional copulas and provide a very flexible way of characterizing dependence in multivariate settings. We apply the model to returns from the G5 and Latin American regions, and document three main findings. First, we discover that models with canonical vines generally dominate alternative dependence structures. Second, the choice of copula is important for risk management, since it modifies the Value-at-Risk (VaR) of international portfolios and produces a better out-of-sample performance. Third, ignoring asymmetric dependence and regime-switching in portfolio selection leads to significant costs for an investor.

Economic Scenario Generation with Regime Switching Models

Economic scenario generators are the basis for generating simulated asset return and economic variable distributions for a range of actuarial applications in insurance and superannuation. Developing an economic scenario generator model for these practical applications is a challenging task mainly because of the dependence and time varying characteristics of the economic series. There are many model structures that can be adopted and historical data is limited given the large number of parameters to be estimated in multivariate models. The desirable features required for a model differ according to the application. In Australia the ERCH model is one of the few models that has been proposed with details available in the public domain. There are various proprietary and commercial models used by consulting firms. This paper reports an analysis of Australian economic and financial data using VAR models, regime switching models for individual series and a multivariate regime switching model calibrated to Australian data.